Squeezing Through A Loophole In The Laws Of Physics To Cool A Drum

NIST researchers applied a special form of microwave light to cool a microscopic aluminum drum to an energy level below the generally accepted limit, to just one fifth of a single quantum of energy. Having a diameter of 20 micrometers and a thickness of 100 nanometers, the drum beat 10 million times per second while its range of motion fell to nearly zero. Image credit: Teufel/NIST

Longer ago than I care to calculate, I was sitting in a lab working on my undergraduate thesis (or, more likely, playing Maelstrom) and listening to my lab partner rattling stuff around in the next room while he looked for something. "I have absolutely no idea where my notebook is!" he yelled.

I cheerfully called back "I can tell you exactly how fast it's moving!" Everything went silent next door, then I heard him walk right up behind my chair. "I hate you," he said.

The joke, old even then, is based on the Heisenberg Uncertainty Principle, one of the best-known ideas from quantum physics. In its most famous form, it says that it's impossible to know both the position and the momentum of a quantum object arbitrarily well; each must have some uncertainty, and the product of the two uncertainties has to be greater than some minimum value. If you knew exactly how fast something was moving, with zero uncertainty, then the uncertainty in its position would need to become infinite. You would have absolutely no idea where it was.

(This is often described as a measurement-perturbing-reality thing, but it's more fundamental, at least in ordinary QM (Bohmian mechanics is another story). It's not that there's a "real" position and momentum that we're not clever enough to measure, it's that it doesn't make sense to talk about those quantities existing at the same time. Here's a cartoon explanation I wrote for TED-Ed.)

My terrible joke also points at something deep, though, which is making news this week. Quantum uncertainty isn't an absolute prohibition on knowing a particular quantity, but a limit on how well you can know two things at once. You can gain knowledge about some property you care about by trading away knowledge about something you're not interested in, and physicists at the National Institute of Standards and Technology have used this to cool a microscopic "drum" to unprecedentedly low temperatures.

The paper on which this is based is titled Sideband cooling beyond the quantum backaction limit with squeezed light," and as you can probably guess from that, there's a lot going on here. The crucial idea, though, is that they've taken a physical object--a microscopic membrane about 0.02 millimeters across and just 100 nanometers thick--and slowed its vibrational motion down to a level that you wouldn't think possible based on a simple application of the uncertainty principle. They were able to do this by exploiting the loophole implicit in the uncertainty principle: they reduced the uncertainty in a quantity they cared about by shifting uncertainty to something else they didn't measure. This process, applied to the microwave-frequency light they used to cool their membrane, is called "squeezing," and it's been known in the optics community for a long time, though this is the first time it's been applied to cooling large objects, with spectacular results.

The first question to ask is probably "What is the limit on cooling this thing, anyway?" For a system like this, it doesn't make sense to talk in terms of degrees in whatever system of units you use, but in terms of quantum physics. The vibration of the membrane has a characteristic energy, and the temperature is a measure of the average energy of a system, so for extremely cold quantum objects, you can talk about the temperature as a multiple of the characteristic energy. Several years ago, the NIST team used their cooling method to reduce the temperature to an average of one-third of the characteristic energy. Since this is a quantum system, only able to occupy a limited set of states, this translates to spending most of its time in the lowest-energy vibrational state (the "ground state"), and only occasionally jumping up to the first excited state (which is one characteristic energy higher). The value of one-third of a quantum is the standard quantum limit for such a system--a simple view suggests you can't get colder than that.

Probability distributions for the eight lowest energy states of a quantum harmonic oscillator. Image from Wikimedia.

Why is there a limit? Well, because of quantum uncertainty. They cool their membrane by pushing on it with microwave-frequency light, and there's necessarily some uncertainty in those light fields. It's not the really famous position-and-momentum uncertainty principle, but the idea is the same: if you try to measure the properties of the light field, you find there are pairs of quantities that can't both be defined at the same time.

The easiest way to talk about this is to talk about it in terms of the amplitude and phase of a classical field--that is, how high the peaks of the wave are, and where the wave starts. These two properties are subject to an uncertainty relationship: the better you measure the amplitude, the less well you know the phase, and vice versa. (If you want to go full-bore quantum, you can convert the amplitude of the wave to the number of photons present; the same relationship holds.) This means both of those things are uncertain, subject to small and unavoidable quantum fluctuations.

Grandpa pushing SteelyKid and The Pip on playground swings. (Photo by Chad Orzel)

Why does this limit cooling? It's a little easier to think about if you imagine the inverse problem: pushing a kid on a swing. In this case, you're trying to increase the energy of the system, and this requires pushing at the right time--that is, the proper phase of the swing. If you always push exactly the same way, right when the kid reaches the farthest backwards point of the swing, they'll quickly be swinging really fast, and scream with delight. If there's a lot of uncertainty in the phase of your push, though, things get messed up--sometimes you push them before they've gotten all the way back, which slows them down, and then their screams will be the unpleasant, annoyed sort.

Cooling an object like the microscopic membranes the NIST team uses is the inverse problem: you're trying to remove energy by pushing on it only at the times when the push will act to slow the motion. The quantum uncertainty in the light field you use to do the "pushing" complicates matters. Loosely speaking, phase fluctuations mean you're sometimes pushing at the wrong time, speeding it up rather than slowing it down, and fluctuations in the amplitude mean sometimes you're not pushing enough to cool it the way you'd like, and sometimes you're pushing too hard and end up speeding it up. When you work through the implications, you find that the cooling you can accomplish is balanced by a heating due to the fluctuations, and that leads to a minimum temperature. In the case of a microscopic membrane cooled by microwave-frequency light, that's one-third of a quantum on average.

So, how can you do better? Well, by trading off uncertainty in one quantity for uncertainty in the other. In the swing-pushing example, it's easy to see that phase fluctuations are more damaging to the process than amplitude fluctuations: if you sometimes push a little harder, and sometimes a little softer, you'll still increase the energy as long as you always push at the right time. Pushing at the wrong time, though, will always cause trouble, regardless of the amplitude. So you can handle a bigger uncertainty in the amplitude of the push, if that gets you a smaller uncertainty in the phase of the pushing.

Amplitude-vs-phase isn't a perfect analogy for what they're doing out in Boulder, but it gets the right basic idea: they manipulate the light hitting their sample in such a way that it reduces the uncertainty in the property that's most damaging to their cooling mechanism, at the cost of increasing the uncertainty in a property that doesn't affect the cooling as much. This process is known as "squeezing" the light, because if you graphically represent the uncertainty as a shaded region on a plot where the horizontal and vertical axes represent the two properties of interest, the uncertainty region gets smaller in one direction and bigger in the other, like a water balloon being squeezed. (I wrote a detailed post about squeezing in 2013, because it's essential to my most significant research paper.)

How do you "squeeze" light? Well, you do something that depends strongly on one of the two quantities you care about--usually something like sending your light into a nonlinear amplifier. Very loosely speaking, this takes a weak signal pulse and amplifies it only when the amplitude fluctuations take it to a high enough level. That cuts out some of the downward fluctuations, giving you a smaller amplitude uncertainty, but since you can't predict exactly when those upward fluctuations will happen, the phase uncertainty gets bigger. (Again, this is a loose analogy, but gets the right idea.) You can even make "squeezed vacuum" by lining up your system to use light that comes out of the nonlinear amplifier, and then sending in no input signal at all--in that case, whatever light comes into your experiment from the amplifier is spontaneously created from vacuum fluctuations that get amplified, subject to the same uncertainty-reducing process.

So, the NIST team's cooling method consists of making squeezed light (I think it's actually squeezed vacuum), and using that in their cooling mechanism. Determining the actual temperature that results is tricky and subtle, and takes up a lot of the paper (and probably a lot of the five years since the ground-state cooling experiment), but at the end of the day, they lowered the energy from the quantum limit of one-third of the characteristic vibrational energy to one-fifth of the energy. That might not seem like a huge change, but it's one of those talking-dog sorts of scenarios: doing it at all is kind of amazing. And at some level this is just a proof-of-principle experiment--with a serious push to optimize the process, they could undoubtedly do even better.

Why are they doing this? Well, for one thing, quantum physics is awesome, and at some level that ought to be enough. In more practical terms, though, the microscopic membranes they use are sensitive to a lot of external perturbations--accelerations of the system, etc. You could imagine using these as part of a sensor system, picking up small changes in the energy of the vibration due to external effects of interest, and for that application, a colder starting state increases the sensitivity of the device.

And, as always when the word "quantum" appears in an abstract, there's a potential to store quantum information in these sorts of devices. These membranes are tiny in everyday terms, but pretty big as quantum systems go, and that makes them robust to some kinds of perturbations. So if you had a quantum bit in some superposition of "0" and "1," you might find that encoding it as a superposition of two states of one of these vibrating membranes was a good way to keep it around for a long time.

But mostly, it's a good story because quantum physics is awesome. The experiment exploits a loophole in one of the most famous quantum results, and uses that to get a big(-ish) object colder than you would've thought possible. It's another window into the fundamental quantum nature of everything around us, and you can never have too many experiments like that.